That reality is called "Let's Go Pikachu and Eevee", but nobody played that. It would be interesting to see if the release of those games (and subsequently, the adaption of their metagame on Showndown) caused any dip in activity for the "regular" Gen VII metagames in here. We tried to make a review panel article on LGPE in The Flying Press, and basically got a response from absolutely everybody that they hadn't played either of the games. They completely failed to leave an impact on the competitive side of Pokémon or on hardcore fans in general.
I can see that a good purge would probably freshen up the competitive metagame a bit. Looking at OU statistics, an awful lot of the used (or even viable) Pokémon were either legendaries or Megas, giving the impression that competitive battling was all about using those special "you-may-see-one-once-in-a-lifetime" kinds of Pokémon according to the lore. The types of Pokémon you could actually catch and train during a regular playthrough were almost absent from the OU scene. It feels a little like Ubers did a few generations ago: Home to legendaries and a handful of exceptionally strong regular Pokémon to fill gaps between them. Standard play could need a little return to, you know, standard Pokémon.
However, eliminating all those Pokémon from existence is a measure that might help a metagame, but it's not good for anything else. It's like removing evolutions from the game entirely just to embrace Little Cup, or doing a game based on Pokémon Contests that has no gyms or battling beyond route trainers. Or one so focused on the collection aspect of Pokémon that the only thing you can do with wild Pokémon is to catch them to earn candy ... oh, wait.
As you said, the fact that there are so many playstyles is one of the great appeals of Pokémon. So the entire concept suffers when a game gets fewer ways to play. In the case of Dexit, competitive play gets a proper scramble, while your options for in-game runs are halved. The upside is felt by the marginal fraction of the playerbase that plays enough competitive to get bored of the current metagame (and who don't want to explore Other Metas with custom banlists), the downside is felt by everyone who has a favourite Pokémon or two from any of the previous seven generations of games. Moreover, that same shakeup of the competitive metagame could be achieved by implementing a simple banlist (OK, as banlists go it would be terribly complex, but you get the idea), without any of the downsides.
At best, the positive aspects of Dexit are a nice side effect that could be achieved in much less disruptive ways. And the negative effects are sorely felt by us all, simply because the games have so many fewer options than they used to. No wonder why most fans don't like the decision at all.